The spherical harmonic transform (SHT) decomposes signals on a sphere
into sets of spherical harmonic coefficients based on the spherical
harmonic functions. As an analog to the Fourier transform, the SHT
extracts scale-dependent features on the sphere and has been
extensively used in analyzing spherical data in various areas of
science, including cosmology and the cosmic microwave background (CMB)
science. For example, by performing SHTs on the CMB anisotropy data and
fitting with the concordance cosmological model (\(\Lambda \) CDM), we are
able to make precise predictions about the cosmological parameters. The
CMB polarization data processing pipeline based on SHTs is also
essential in detecting primordial gravitational waves. Recent
developments in cosmological surveys in CMB temperature and
polarization anisotropies [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]} pose
new challenges to data analysis, which usually requires processing a
large amount of CMB mock data. Therefore, it is important to reduce the
time cost of SHTs on a large number of spherical maps.
